Application of the nonlocal and nonlinear models of elasticity for description and physical interpretation of stress-strain state in vicinity of singular points

摘要

We explore the fracture mechanics problems and show that the singularity in the mechanics of fracture is a formal result, related to the inconsistency of the boundary conditions, which determine the properties of a singular corner point in the general case. Using the gradient theory of elasticity, we provide the consistency of the boundary conditions at the crack tip and show that, as a result, we can construct a non-singular solution in the neighborhood of singular points, that have classical asymptotic behavior on infinity. Consistency of boundary conditions can be realized using gradient theory of elasticity. It is shown that the non-singular solutions in the neighborhood of crack tips can be interpreted as an elastic deformation field in the classical elasticity with local nonlinearity.